Fig.1

Schematic diagram of the shape of the tapered fiber"

Fig.2

Cladding mode distributions of conventional LPFG and LPFGs with different taper diameters"

Fig.3

Optical energy distributions along the transmission direction of the LPFG with a period of 450 $\mu$m written in the tapered fiber with a thinnest diameter of 90 $\mu$m"

Fig4.

Transmission spectra of the LPFG written in the tapered fiber with a thinnest diameter of 100 $\mu$m with a period of 500 $\mu$m at different surrounding refractive index and dependence of the resonance wavelengths of LP$_{06}$ mode on the surrounding refractive index"

Fig.5

Transmission spectra of the LPFG written in the tapered fiber with a thinnest diameter of 90 $\mu$m with a period of 450 $\mu$m at different surrounding refractive index and dependence of the resonance wavelengths of LP$_{06}$ mode on the surrounding refractive index"